Ex10 12

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.12}$

What is the maximum possible amount of entanglement, as measured by the von Neumann entropy, over all pure states of a bipartite quantum system $A\otimes B$ where $A$ has dimension $n$ and $B$ has dimension $m$ with $n \geq m$.